This clash was the first time that Jones had been at Stoke City since his departure in November 2019, which marked the end of a spell that saw him only pick up seven wins from 38 games as the Potters boss.
In truth, the Hatters never really got going as Stoke dominated the game from start to finish and on another day they even could have added a couple of more to the scoresheet.
The result means that the Potters have now earned back to back victories after the 1-0 win over Sheffield Wednesday in mid-week meaning that they remain in ninth place, but now they are only five points adrift of the play-off places with 15 games remaining.
Meanwhile, the loss for Luton marks only one win in seven in all competitions now for them with survival not a guarantee as they are only six points clear of safety now.
Story of the game
The hosts made a bright start and were close to breaking the deadlock almost immediately but Powell's snapshot from range arrowed narrowly over Simon Sluga's crossbar.
Despite dominating the opening stages, the Potters really struggled to break past the visitors' line of defence.
However, two minutes later the hosts went a goal to the good when Fletcher found himself one on one after beating captain Sonny Bradley on the edge of the box.
But instead of going for goal himself, he took the unselfish option of squaring the ball to the free Powell who had the easy task of tapping the ball home.
After the opener, Michael O'Neill's side continued to maintain complete control and were the ones that looked the more threatening to get the next goal without really carving out any opportunities.
Then shortly after the interval the home side's dominance seemed to be continuing as a good free-kick by Jordan Thompson found the head of Harry Souttar, but his glancing header landed into the arms of Sluga.
Then three minutes later the Hatters found themselves in a rare attack when James Collins was found in space down the left-hand side, but his ball across goal was parried away to safety by Angus Gunn.
Fletcher then had a good opportunity to double his side's advantage when he met Powell's cross from the left at the near post, but his header was powered well wide of the mark.
A couple of minutes later, Sluga had to make a very smart save to deny Powell from grabbing a brace when his cross from deep evaded everyone in the box and seemed to be destined for the corner, but Sluga managed to recover away to turn the ball away.
When chasing the game, the visitors were really struggling to get into the positions to get meaningful shots away as just after the hour mark, Jordan Clark could only have a speculative shot from distance that was comfortably held by Gunn.
Then a minute later, the three points were pretty much wrapped up when Powell did get a deserved second as he rose highest to a Joe Allen cross from the right and managed to powerfully nod the ball into the roof of the net.
Seven minutes later the Potters looked to extend their lead when Danny Batth latched on to the end of a deep Tommy Smith free-kick but his header sailed just over the crossbar.
Things were close to getting disastrous for Luton and Sluga who failed in seeing the ball out of play after being put under pressure by Sam Clucas, something which nearly cost him, but the substitute's effort from a tight angle bounced wide of the near post.
Three minutes later though, Stoke did get the third that they had been looking for and deserved when a defensive mix up saw Clucas get in down the left-hand side and he laid the ball off to Fletcher who tapped the ball home for his eighth of the campaign.
It should have got even worse for Jones in the 83rd-minute mark when a Smith inviting cross from the right found substitute Sam Vokes unmarked at the back post, but his well-connected header was brilliantly clawed away by Sluga.
Four minutes later Sluga was really the reason to prevent the scoreline from becoming humiliating as he made a good block with his legs to stop substitute James McClean from finding the net at the back post.
Impressive performance that Potters will look to achieve on a consistent basis
There is no doubt today that for 90 minutes Stoke were absolutely magnificent and were well worthy of the three points.
From the off, they played with a high tempo while also not really allowing the Hatters time on the ball especially in dangerous areas.
The only negative in the first period that you could pick out was that they did not test Sluga enough but the same could not have been said about the second 45 minutes as particularly in the final 20 minutes, the hosts may be disappointed to have not had more.
After recently only just coming off an 11 game winless run, it is this kind of performance for the remainder of the season that they will look to emulate.
If they manage to do this with them only being five points adrift of the play-off positions, there is no reason to why they cannot be contending to finish inside the top six come the end of the season.
Need to improve attacking threat on the road if they look to survive
After not managing to net at the Bet365 Stadium, it remains that Luton have only netted seven goals in the league away from home so far this season, with five of these goals coming in different 1-0 wins.
Today, Jones' side really did not provide a threat on the attacking side of things leaving Southampton loanee Gunn with very little to do.
Throughout the encounter, they just tried the same thing which was to get balls into the dangerman Collins, but ultimately the service from deep positions did not have enough quality for this to be effective.
Therefore, arguably at half time, Jones should have changed things up in order to try to get his side going and for them to show to have an attacking threat.
A way in which to do this was to bring on new signing Elijah Adebayo earlier than he in fact did because this was have provided the visitors with another presence up top and another body forward.
This would mean that it would give more chance for a Hatters player to get on the end of deliveries from wide positions.
Consequently, the refusal to change how his team play has got to be considered a factor to why Luton lost today and the blame for that must come down to Jones.
The lack of goals that his side do score on the road must be seen as a concern to the 47-year-old and with them entering the late stage of the season, it is something that they must significantly work on in the training ground if they wish to remain in the Championship for a second season running.
Star Player- Nick Powell
He sat in just behind lone forward Fletcher and throughout his spell on the pitch, he linked up really well with the 33-year-old.
When the experienced striker dropped in deep which is something that he was seen often doing, Powell wandered into the central striker role to still maintain that the Potters had an attacking outlet.
This in itself shows that the two players have formed a really good understanding and working relationship with each other.
Not only this but his two goals which were significant in deciding the outcome of a game were taken really well as he got in good attacking positions which allowed him on both occasions to tuck the ball away.
After his brace today he is now up to ten for the season in the league something that will no doubt encourage O'Neill and as long as he can stay clear of any long term injuries, it is certain that Powell will be a force to be reckoned with as the Potters look to make a late push for a play-off finish.